Nonlinear superpositions and Ermakov systems

Abstract

The theory of superposition rules for solutions of a Lie system of first-order differential equations is extended to deal with analogous systems of second-order and the theory is illustrated with the very rich example of Ermakov-like systems.

18 pages

References in corpus (5)

• Superposition rules, Lie theorem and partial differential equations
• Riccati equation, Factorization Method and Shape Invariance
• A remark on rational isochronous potentials
• The nonlinear superposition principle and the Wei-Norman method
• Isoperiodic classical systems and their quantum counterparts

Cited by in corpus (6)

• A nonlinear superposition rule for solutions of the Milne--Pinney equation
• Superposition rules for higher-order systems and their applications
• Quasi-Lie schemes: theory and applications
• Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping
• Integrability of Lie systems and some of its applications in physics
• Superposition rules and second-order differential equations